Can white force a draw somehow from this position using only his knight and king?
No. Even assuming it's White's move, Black can force mate in five moves according to the computer. But you don't really need to calculate that much since Black's material advantage is so overwhelming.
The only hope would be a stalemate, but it is unlikely. To achieve that, the knight would have to be pinned or lost, but I don't see how you can force that: if it got pinned, Black could just unpin it in the next move if necessary, or simply capture it. Even trading the queen for the knight, the position would still be easily won by Black. Black only needs to make sure that if they take the knight, they don't cause an immediate stalemate (that would be Black's blunder, not something forced by White).
Here's one of the possible lines that end with mate in five:
8/p7/6k1/2p5/6r1/2N4q/1K6/8 w - - 0 1 1. Kc2 Rc4 2. Kd1 Qd3+ 3. Ke1 Rxc3 4. Kf2 Rc2+ 5. Ke1 Qe2#
It is not possible to force a draw. Even if Black somehow lost both pawns and his rook, the resulting endgame is still won for Black.
[FEN "8/8/6k1/8/8/2N4q/1K6/8 w - - 0 1"] 1. Kc2 Qg4 2. Nb1 Qd4 3. Nc3 Kf5 4. Ne2 Qe3 5. Nc3 Ke5 6. Kb2 Qd3 7. Na4 Qb5+ 8. Ka3 Kd4 9. Nb2 Ke3 10. Nc4+ Qxc4 11. Kb2 Qb4+ 12. Ka2 Kd3 13. Ka1 Kc3 14. Ka2 Qb2#
Black has Rg2, Qh1. The only way that's not checkmate is if white interposes the knight, but then the knight is pinned and can be taken.